In the related art, an NOx occlusion reduction type catalyst is known as a catalyst which reduces and purifies a nitrogen compound (NOx) in an exhaust gas discharged from an internal combustion engine. When the exhaust gas is under a lean atmosphere, the NOx occlusion reduction type catalyst occludes the NOx contained in the exhaust gas. When the exhaust gas is under a rich atmosphere, the NOx occlusion reduction type catalyst detoxifies the occluded NOx through reducing and purifying with hydrocarbon contained in the exhaust gas, and discharges the NOx. For this reason, in a case where the NOx occlusion amount of the catalyst reaches a predetermined amount, in order to recover NOx occlusion capacity, it is necessary to regularly perform the so-called NOx purge which makes the exhaust gas be in a rich state by a post injection or an exhaust pipe injection (for example, see JP-A-2008-202425).
In addition, there is proposed a technique for calculating, based on an output of a sensor disposed downstream of an NOx absorbent, at least one of the maximum amount of NOx absorption of the NOx absorbent and an NOx absorption rate in the NOx absorbent and for determining that the NOx absorbent has deteriorated when the calculated maximum amount of NOx absorption or the NOx absorption rate is smaller than the determination value (for example, see JP-A-2002-266629).